Lozenge Land

Read a flat tiling as deep stone, and cut the cheapest stairs that let the water climb it.

The Lozenge Land board

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Grades
3–6
Subjects
Shapes & Space, Logic
Kind
Puzzle

What it is

The board is a tiling of three kinds of rhombus, and it is also a heap of stone blocks seen from one corner: pale floors, a sunlit wall and a shaded one. Water starts on the lowest floor and climbs any step of one block, but a drop of two is a cliff it cannot get up. Add or take away blocks until water reaches every floor, changing no more blocks than the aim allows.

The rules

A small land of stone, green on the ground, with a spike three blocks high standing dry at the back. Dots mark the corners where all three kinds of face meet. A finger taps the dot on top of the spike and a block lifts away; it taps the same dot again and the block comes back.
Tap on a dot to add or remove a block.
A terrace of stone standing two blocks over a green floor. A block is laid at its foot, its top green like the floor it rose from, and then the grass climbs from it up onto the terrace, a few squares at a time.
Green grass will grow on a block that you can walk to without climbing.
The stone with the spike again, and a count over it: 0 of 2 blocks. A finger takes two blocks off one side of the spike and the grass climbs onto it, but the other side still stands too high and dry. The count reads 2 of 2 and turns amber; the finger tries one more block and the count shakes; the stone turns grey.0/21/22/2
You win if you can make grass grow on all the blocks. Unfortunately, you don't get many taps.

What it gives you to practise

Seeing depth in a flat drawing, and holding on to it. The same rhombuses read as a heap or as a hollow, and the trees standing on the floors are there to say which way is up. Then planning: a block can only sit where the blocks behind it and beside it hold it up, so the cheapest stair is rarely the first one that comes to mind. On every board the aim is the true minimum, proved by the computer before the stone is shown — the random stones too — so matching it is a real result.

In a classroom

The board prints as line art with the grass taken off, so finding where the water stops becomes the paper puzzle and a pencil marks the blocks to change. The first stones in Level I need a block or two; a couple of those, before anybody tries a ten-across stone, is enough for a class to agree on which way is up.

Share or embed

The whole puzzle at one address, with every board in it. Whoever opens it stays inside it, and their progress stays in their own browser.

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